If I were in your shoes, here's how I would approach it. You didn't mention a specific protest movement, so I will use BlackLivesMatter as an example.
I would first reach out to a local chapter of BLM to learn more about their short-term and long-term goals, and also probably try to attend as many events as I can.
The purpose of this would be to understand where the organization is going and what obstacles are currently stopping them. Then, maybe I can leverage my software skills to help.
But, it's important for me to first understand what the need is, because that's how you know you can have the most effect.
Maybe BLM needs AI facial recognition or maybe they just need a reliable CRUD app to reduce operational costs.